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Derivation of boundary condition for turbulent dissipation

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Old   August 23, 2022, 02:12
Question Derivation of boundary condition for turbulent dissipation
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Sangho Ko
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Hello everybody!

I'm wondering how below boundary condition is derived.
\epsilon =\frac{C_{\mu }^{0.75}k^{1.5}}{L}

I know below formula.
\epsilon=\frac{C_{\mu }k^{2}}{\nu _{T}}.

But I don't know how upper formula is derived from lower formula.

Thank you~!
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Old   August 23, 2022, 02:52
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The first formula is the so-called equilibrium law. It is not an exact result but one worth knowing. There was a somewhat recent discussion in Annual Revs. Fluid Mechanics. People often use this formula to calculate a reasonable value for epsilon to be applied as an inlet boundary condition. For super accurate simulations, you have to get the real value of epsilon via even more accurate simulation or measure it directly.


The second formula is the k-epsilon turbulence model itself.
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Old   August 23, 2022, 03:06
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Quote:
Originally Posted by LuckyTran View Post
The first formula is the so-called equilibrium law. It is not an exact result but one worth knowing. There was a somewhat recent discussion in Annual Revs. Fluid Mechanics. People often use this formula to calculate a reasonable value for epsilon to be applied as an inlet boundary condition. For super accurate simulations, you have to get the real value of epsilon via even more accurate simulation or measure it directly.


The second formula is the k-epsilon turbulence model itself.
Aha that is just derived from dimensional analysis.

Thank you~!
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boundary condition, dissipation rate, mixing length, turbulent intensity

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